Non-significant coefficient after adding variable

[laura andrada]

hi, im running an OLS regression to know the rrelation between moving and income. First i just used the explanatory variable "moving", secondly I used "moving" and "change of city" as explanatory variables (Both explanatory are dummy variables). In the first regression the "moving" variable was positive and significant, however in the second none of the explanatory variables are significant. I'm not quite sure how to interpret these change in the results. Can someone help me? My sample size is 6000 for which 1000 people moved and around 500 change city during the move.

My results are the following (Standard errors are in parenthesis):
1.

Log(Income)
Moving	0.0572*** (0.0220)

2.

Log(income)
Moving	0.0378 (0.0303)
Change of city	0.0398 (0.0389)

I appreciate all the help you can provide me

[Marcos Almeida]

Welcome to the Stata Forum/Statalist.

Please prefer to present command and output as recommend in the FAQ.

This is the best way to share a truly "readable" information on your model and to entice helpful replies.

That said, it seems your "crude" model, albeit statistically significant in terms of p-value, provided a tiny coefficient. Tiny as it is, when adjusted for other predictors, it gets a p-value which infers the coefficient for moving is not significantly different from zero.

Hopefully that helps.

[Carlo Lazzaro]

Laura:
Marcos gave helpful advice.
Your first model might well suffered from omitted variable bias (and, if so, any conclusion about the significance of your unique predictor will be biased).
If the literature in your reserch field reccomends you to do so, you may want to interact the predictors in your second model:

regress Log_(Income) i.Moving##i.Change_of_city

That said, I would be more worried about the risk of endogeneity (reversal causation) in your model: is -Log_(Income) a possible explanation of people moving from, say, outskirts to (down)town?

[Richard Williams]

Like the others, my first thought is omitted variable bias. Two other possibilities:

• Multicollinearity -- are moving and change of city highly correlated? If so it may be hard to separate their effects and both wind up insignificant.
• Loss of cases -- did the N drop as you added more variables, because of missing data on the new variables? That can cause loss of statistical power.

From the info you gave we can't address either of those Qs. But I'd be surprised if there wasn't a strong correlation between your vars.

[laura andrada]

Thanks for the advise.
I know my variable is endogene. Therefore, im only adressing correlation, Moreover, N did not drop in this case.
I also control for other socioeconomic variables of the individual like gender, migration among others (13 other control variables) and use fixed effects.

[Marcos Almeida]

Something also to notice, still on the same verge (in terms of collinearity) as pointed out in #4, the SEs are basically the same size of the coefficients...

[Carlo Lazzaro]

Laura:
I fail to get how limiting your analysis at correlation (but you were seemingly describe a fixed-effect regression model in your last post, thoug) can sheleter your results from endogeneity bias.
I woud have rather expected a sketch of an instrumental regression.

[Richard Williams]

Again, I think those vars are highly correlated. If you are a 0 on moving I assume you are also a 0 on change city. And if you are a 1 on moving I assume you are often a 1 on change city. It may therefore be very hard to separate the effects of the two. You might try a joint test of the two to see if they are together significant, e.g.

test moving=changecity

[laura andrada]

thanks for the comments